An ominous World Health Organisation (WHO) forecast said on Tuesday that with so many people now spreading the virus, the number of Ebola cases could start doubling every three weeks.
Mr Obama spoke after briefings in Atlanta with doctors and officials from the Centres for Disease Control and Prevention and Emory University – where three US aid workers with the disease were successfully treated.
The president said: “If the outbreak is not stopped now, we could be looking at hundreds of thousands of people affected, with profound economic, political and security implications for all of us.”
Mr Obama also called on other countries to begin supplying more health workers, equipment and money.
At least 2,400 people have died in the West African outbreak, mostly in Liberia.
Nearly 5,000 people have fallen ill in Liberia, Sierra Leone, Nigeria and Senegal since the outbreak was first recognised in March.
The WHO has said it anticipates that the number of people with the disease could rise to more than 20,000 and end up costing nearly $1 billion (£600 million) to contain.
Mr Obama described the task as “daunting” but said there was hope in the fact that “the world knows how to fight this disease”.
His expression grim, he described the “gut-wrenching” scene of a family in Liberia.
The father had died, the mother was cradling a sick five-year-old, and her ten-year-old was dying too. The family had reached a treatment centre but could not get in.
“These men and women and children are just sitting, waiting to die, right now.” Mr Obama said. “It doesn’t have to be this way.” The US is promising to deliver 17 100-bed treatment centres to Liberia, where contagious patients often sit in the streets, turned away from packed Ebola units.
The Pentagon expects to have the first centres open within a few weeks.
White House press secretary Josh Earnest said 3,000 troops being sent to the region would not provide direct care to Ebola patients.
In addition to delivering the 17 treatment facilities, troops will help train as many as 500 local healthcare workers a week.
Among the other initiatives, the US military will set up a headquarters in Liberia’s capital, Monrovia, build a regional transportation and staging base in Senegal to co-ordinate the contributions of other allies and provide home healthcare kits to hundreds of thousands of households, designed to help healthy people caring for Ebola-stricken family members.
It will also carry out a home- and community-based campaign to train local populations on how to handle exposed patients.
Médecins Sans Frontières, which has sounded the alarm for months, also welcomed the US effort but said it must be put into action immediately – and that other countries must follow suit because the window to contain the virus is closing.
Brice de le Vingne, the group’s director of operations, said: “The response to Ebola continues to fall dangerously behind, and too many lives are being lost.
“We need more countries to stand up, we need greater concrete action on the ground, and we need it now.”
Dr Kent Brantly, an American physician who survived Ebola contracted while working in Liberia, met Mr Obama at the White House on Tuesday. He is one of three aid workers with Ebola who have been treated at Emory in recent months.
Later, he told a packed Senate hearing: “We must move quickly and immediately to deliver the promises that have been made.”
The UN Security Council will hold an emergency meeting on the crisis, and the head of the United Nations said that the General Assembly will follow up with a high-level meeting next week as the world body “is taking the lead now” on the international fight.
In Monrovia, Boima Folley runs a sport materials shop and said he would welcome the US military response.
He said: “We have been praying to get the disease wiped out of our country, so if the US troops will help us get that done, we should be happy.”